1. Field of the Invention
The present invention is directed to an optical element, the method of making the optical element, an optical system using the optical element for an optical apparatus (e. g., a camera, microscope, telescope or photolithographic apparatus such as a stepper, etc.), and a method for calculating the birefringence of the optical element.
2. Description of the Related Art
Calcium fluoride, strontium fluoride and barium fluoride, which are fluoride crystals (single crystals) used as optical element materials, have a low refractive index compared to ordinary optical glass, and also show little dispersion (wavelength dependence of the refractive index); accordingly, such materials are useful for color aberration correction in optical systems.
In particular, calcium fluoride is easy to obtain, and can be obtained even as large-caliber single crystals with a diameter of .phi. 150 mm or greater.
Such fluoride crystals (single crystals) belong to the cubic crystal type, and are optically isotropic bodies. These materials are suitable as materials for optical elements such as lenses, etc. Fluoride crystals have long been widely used as materials of camera lenses, microscope lenses and telescope lenses, etc.
Birefringence is a phenomenon in which the refractive index varies according to the direction of polarization of the light or other electromagnetic waves. Ordinarily, this is expressed as the light path difference (called "retardation") that occurs when the light passes through a unit length of the substance in question, and is given in units of nm/cm.
Furthermore, as another method of expressing birefringence, this phenomenon is also sometimes expressed as the difference (n1-n2) between the refractive index n1 with respect to light having a certain direction of polarization and the refractive index n2 for light with a direction of polarization that is perpendicular to the above-mentioned direction of polarization.
Furthermore, the refractive index n0 in a state in which no external force is acting on the substance in question is affected by external forces so that the refractive index changes. In cases where this change is dependent on the direction of polarization, the amounts of change in the refractive index are expressed as .DELTA.n1 and .DELTA.n2, and the difference between these amounts of change, i. e., (.DELTA.n1-.DELTA.n2), is also sometimes called "birefringence".
In cases where birefringence is caused by strain, this birefringence is also commonly called "strain". Moreover, crystals with cubic crystal systems inherently lack birefringence, but may have birefringence as a result of the effects of electromagnetic fields and stress.
Specifically, in the case of the above-mentioned fluoride crystals (single crystals), birefringence is generated as a result of the effects of stress. For example, considerable birefringence is present in currently manufactured fluoride crystals as a result of thermal stress occurring in the manufacturing process. Furthermore, the value of this birefringence is at least about 5 nm/cm, and may commonly reach 10 mn/cm or greater in fluoride crystals with a diameter of .phi. 100 mm or greater.
Accordingly, even if an attempt is made to minimize the aberration of an optical system using a fluoride crystal (single crystal), the birefringence of the fluoride crystal arising from the effects of stress is an impediment. As a result, satisfactory optical performance often can not be obtained in the optical system.
Furthermore, if countermeasures such as an extreme lengthening of the annealing time in the fluoride crystal manufacturing process, etc., are adopted in order to reduce the birefringence of fluoride crystals (single crystals) used in optical elements or optical systems, delivery dates are delayed (i. e., the productivity drops), and costs are increased.
In recent years, there has been a rapid development of lithographic techniques for inscribing integrated circuit patterns on wafers. Demand for higher integration of integrated circuits continues to grow. In order to realize such higher integration, it is necessary to increase the resolving power of stepper projection lenses.
The resolving power of a projection lens is governed by the wavelength of the light used and the NA (numerical aperture) of the projection lens. The resolving power can be increased by shortening the wavelength of the light used or increasing the NA (increasing the caliber) of the projection lens.
First, shortening of the wavelength of the light used will be discussed. The wavelengths used in steppers have already advanced to the g line (wavelength: 436 nm) and i line (wavelength: 365 nm). In the future, when even shorter-wavelength KrF excimer laser light (wavelength: 248 nm) and ArF excimer laser light (wavelength: 193 nm), etc., come into use, the use of optical glass in optical systems will become virtually impossible from the standpoint of transmittance.
Accordingly, synthetic silica glass or calcium fluoride is commonly used as an optical element material in the optical systems of excimer laser steppers.
Next, increasing the caliber of such elements will be discussed. Here, it is not simply a question of better results with a larger caliber. In regard to the materials of optical elements used in the optical systems of excimer laser steppers, it is necessary that single crystals be used in the case of calcium fluoride.
Furthermore, as the performance of steppers has improved, there has recently been a demand for large-caliber calcium fluoride single crystals with a caliber of around .phi. 120 mm to .phi. 250 mm. Such calcium fluoride single crystals have a low refractive index compared to ordinary optical glass, and also show little dispersion (wavelength dependence of the refractive index). Accordingly, such materials are extremely effective in the correction of color aberration. Furthermore, such materials can easily be obtained in the marketplace, with large-caliber single crystals having a diameter of .phi. 120 mm or greater also being obtainable.
Calcium fluoride single crystals which have such advantages have long been used as lens materials in cameras, microscopes and telescopes in addition to being used as optical materials in steppers.
Furthermore, single crystals of barium fluoride and strontium fluoride, which are fluoride single crystals other than calcium fluoride single crystals, belong to the same cubic crystal type, and have similar properties; accordingly, the uses of these crystals are also similar to those of calcium fluoride single crystals.
Such fluoride single crystals can be manufactured by a method known as the Bridgeman method, the Stockberger method, or the "pull-down" method.
Here, a method for manufacturing calcium fluoride single crystals by the Bridgeman method (one example) will be described.
In the case of calcium fluoride single crystals used in the ultraviolet or vacuum ultraviolet region, natural fluorite is not used as a raw material; instead, the general practice is to use high-purity raw materials manufactured by chemical synthesis.
The raw materials can be used "as is" in a powdered state. In such a case, however, the volume decrease upon melting is severe. Ordinarily, therefore, semi-molten raw materials or pulverized products of the same are used.
First, a crucible filled with the above-mentioned raw material is placed in a growth apparatus, and the interior of the growth apparatus is maintained at a vacuum of 10.sup.-3 to 10.sup.-4 Pa.
Next, the temperature inside the growth apparatus is elevated to a temperature above the melting point of calcium fluoride (1370.degree. C. to 1450.degree. C.) so that the raw material is melted. In this case, control by means of a constant power output or high-precision PID control is performed in order to suppress fluctuations in the temperature inside the growth apparatus over time.
In the crystal growth stage, the crucible is lowered at a speed of approximately 0.1 to 5 mm/h, so that crystallization is gradually caused to occur from the lower part of the crucible.
When crystallization has occurred up to the upper portion of the melt, crystal growth is completed, and a simple gradual cooling process is preformed, with sudden cooling being avoided so that the grown crystal (ingot) does not crack. When the temperature inside the growth apparatus has dropped to room temperature, the apparatus is opened to the atmosphere, and the ingot is removed.
Ordinarily, a graphite crucible is used in this crystal growth, and a pencil-shaped ingot with a conical tip is manufactured. In this case, a single crystal can be formed by growing the crystal from the area of the tip end of the conical part positioned at the lower end of the crucible.
Furthermore, if necessary, there is also a technique in which the direction of crystal growth is controlled by placing a seed crystal in the above-mentioned tip end portion; however, if the diameter of the ingot exceeds .phi. 120 mm, control of the orientation of crystal growth becomes extremely difficult.
Generally, in cases where a fluoride single crystal is manufactured by the Bridgeman method, it is considered that there is no preference in the direction of growth, so that the horizontal plane of the ingot is a random plane in each crystal growth process.
Since there are extremely large amounts of residual stress and strain in the ingot removed from the crucible, the ingot is subjected to a simple heat treatment "as is".
The fluorite single crystal ingot thus obtained is cut to an appropriate size according to the desired product. Here, the ingot is naturally cut horizontally (annular cut) in order to cut out a material for manufacturing a larger optical element (lens, etc.) from the ingot in accordance with the desired product. Then, the material thus cut out is subjected to a heat treatment in order to improve the quality of the material.